Accelerating Growth and Size-dependent Distribution of Human Activities Online

Research on human online activities usually assumes that total activity T increases linearly with active population P , that is, T ∝ P (γ = 1). However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship T ∝ P (γ > 1) is in fact ubiquitous in online activities such as micro-blogging, news voting and photo tagging. We call the pattern “accelerating growth” and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate γ associates with a scaling parameter b in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is novel and worth further exploration.